Question

The following triplets represent the length of sides of the triangle. Use the Pythagoras theorem to check which triplets would make the right triangle.

Note all measures are in cm:

(a)$15,20,25$

(b)$8,9,10$

(c) $2.5,6.5,6$

(d)$16,12,20$

(e)$17,15,8$

(f)$13,14,8$

(g)$7,24,25$

(h)$8,7,12$

Answer 1

Step 1 : Checking if $15,20,25$ will make the right triangle.

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse.

${\left(\text{hypotenuse}\right)}^2={\left(\text{perpendicular}\right)}^2+{\left(\text{base}\right)}^2$

$$\begin{gathered} {\left(25\right)}^2={\left(15\right)}^2+{\left(20\right)}^2 \\ 625=225+400 \\ 625=625 \end{gathered}$$ ( Note: longest side is hypotenuse)

Hence, it forms right angled triangle

Step 2 : Checking if $8,9,10$ will make the right triangle.

Since, ${\left(\text{hypotenuse}\right)}^2={\left(\text{perpendicular}\right)}^2+{\left(\text{base}\right)}^2$

$$\begin{gathered} {\left(10\right)}^2={\left(8\right)}^2+{\left(9\right)}^2 \\ 100=64+81 \\ 100\ne 145 \end{gathered}$$ ( Note: longest side is hypotenuse)

Hence, it doesn't forms right angled triangle

Step 3 : Checking if $2.5,6.5,6$ will make the right triangle.

Since, ${\left(\text{hypotenuse}\right)}^2={\left(\text{perpendicular}\right)}^2+{\left(\text{base}\right)}^2$

$$\begin{gathered} {\left(6.5\right)}^2={\left(6\right)}^2+{\left(2.5\right)}^2 \\ 42.25=36+6.25 \\ 42.25=42.25 \end{gathered}$$ ( Note: longest side is hypotenuse)

Hence, it forms right angled triangle

Step 4 : Checking if $16,12,20$ will make the right triangle.

Since, ${\left(\text{hypotenuse}\right)}^2={\left(\text{perpendicular}\right)}^2+{\left(\text{base}\right)}^2$

$$\begin{gathered} {\left(20\right)}^2={\left(16\right)}^2+{\left(12\right)}^2 \\ 400=256+144 \\ 400=400 \end{gathered}$$ ( Note: longest side is hypotenuse)

Hence, it forms right angled triangle

Step 5 :Checking if $17,15,8$ will make the right triangle.

Since, ${\left(\text{hypotenuse}\right)}^2={\left(\text{perpendicular}\right)}^2+{\left(\text{base}\right)}^2$

$$\begin{gathered} {\left(17\right)}^2={\left(15\right)}^2+{\left(8\right)}^2 \\ 289=225+64 \\ 289=289 \end{gathered}$$ ( Note: longest side is hypotenuse)

Hence, it forms right angled triangle

Step 6 :Checking if $13,14,8$ will make the right triangle.

Since, ${\left(\text{hypotenuse}\right)}^2={\left(\text{perpendicular}\right)}^2+{\left(\text{base}\right)}^2$

$$\begin{gathered} {\left(14\right)}^2={\left(13\right)}^2+{\left(8\right)}^2 \\ 196=169+64 \\ 196\ne 233 \end{gathered}$$ ( Note: longest side is hypotenuse)

Hence, it doesn't forms right angled triangle

Step 7 :Checking if $7,24,25$ will make the right triangle.

Since, ${\left(\text{hypotenuse}\right)}^2={\left(\text{perpendicular}\right)}^2+{\left(\text{base}\right)}^2$

$$\begin{gathered} {\left(25\right)}^2={\left(24\right)}^2+{\left(7\right)}^2 \\ 625=576+49 \\ 625=625 \end{gathered}$$ ( Note: longest side is hypotenuse)

Hence, it forms right angled triangle

Step 8 :Checking if $8,7,12$ will make the right triangle.

Since, ${\left(\text{hypotenuse}\right)}^2={\left(\text{perpendicular}\right)}^2+{\left(\text{base}\right)}^2$

$$\begin{gathered} {\left(12\right)}^2={\left(8\right)}^2+{\left(7\right)}^2 \\ 144=64+49 \\ 144\ne 113 \end{gathered}$$ ( Note: longest side is hypotenuse)

Hence, it doesn't forms right angled triangle