In the figures- perimeter of - ABC - perimeter of - PQR- Find the area of - ABC-

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Area of a Triangle

In the figure...

Question

Question 85

In the figures, perimeter of $Δ A B C$ = perimeter of $Δ P Q R$ . Find the area of $Δ A B C .$

Open in App

Solution

Given, perimeterof $Δ A B C$ = perimeter of $Δ P Q R$
$∴$ Perimeter of $Δ P Q R = 14 + 6 + 10 = 30 c m [∵$ perimeter of triangle = sum of all sides]
Now, perimeter of $Δ A B C = A B + B C + C A$
30 = AB + BC + AC
$\Rightarrow 30 = A B + 5 + 13 \Rightarrow 30 = A B + 18 \Rightarrow A B = 30 - 18 = 12 c m$

Triangle with sides 5, 12, 13 is a right angled triangle.
$∴$ Area of $Δ A B C = \frac{1}{2} \times B a s e \times H e i g h t$
$= \frac{1}{2} \times 5 \times 12 = 5 \times 6 = 30 c m^{2}$

Suggest Corrections

Similar questions

Q. If the

Δ A B C \sim Δ P Q R,

perimeter of

Δ A B C = 32 c m,

perimeter of

Δ P Q R = 48 c m

and

P R = 6 c m,

then find the length of

A C .

In the given figure, ΔABC is congruent to ΔPQR.

What is the perimeter of ΔABC?

Q. In

Δ A B C

A B = 5

B C = 6

A C = 7

Δ P Q R - Δ A B C

. Perimeter of

Δ P Q R

360

. Find PQ, QR and PR.

Δ A B C Δ P Q R

for the correspondence

A B C \leftrightarrow P Q R

. If the perimeter of

Δ A B C

12

and the perimeter of

Δ P Q R

20

, then

A B : P Q =

______

In the adjoining figure, $Δ A B C$ is a triangle and through A, B, C lines are drawn, parallel respectively to BC, CA and AB, intersecting at P, Q and R. Prove that the perimeter of $Δ P Q R$ is double the perimeter of $Δ A B C$ .

Join BYJU'S Learning Program

Question 85 In the figures, perimeter of ΔABC = perimeter of ΔPQR. Find the area of ΔABC.

Question 85

In the figures, perimeter of $Δ A B C$ = perimeter of $Δ P Q R$ . Find the area of $Δ A B C .$