Question

A grassy land in the shape of a right angled triangle has its hypotenuse $1$ metre more than twice the shortest side. If the third side is $7$ metres more than the shortest side. The sides of the grassy land are:

• A. $8$m, $17$m, $15$m
• B. $2$m, $16$m, $13$m
• C. $10$m, $4$m, $5$m
• D. $7$m, $10$m, $14$m

Answer 1

Answer: (A)

$8$m, $17$m, $15$m

Let the length of the shortest side be $x$ meters. Then,
Hypotenuse = $(2x+1)$ meters, Third side = $(x+7)$ meters
(Hyppotenuse)${}^2$ = sum of the square of the remaining two sides ....[By pythagorous theroem]
$\Rightarrow (2x+1{)}^2=x^2+(x+7{)}^2$
$\Rightarrow 4x^2+4x+1=2x^2+14x+49$
$\Rightarrow 2x^2-10x-48=0$
$\Rightarrow x^2-5x-24=0$
$\Rightarrow x^2-8x+3x-24=0$
$\Rightarrow x(x-8)+3(x-8)=0$
$\Rightarrow (x-8)(x+3)=0$
$\Rightarrow x=8,-3$
$\Rightarrow x=8$ [$\because x=-3$ is not possible]
Hence, the lengths of the sides of the grassy land are $8$ m., $17$ m. and $15$ m.