Question

The difference between the sites at right angles in a right angled triangle is 14 cm. The area of the triangle is 120 cm². Calculate the perimeter of the triangle?​

Answer 1

Given:

• Difference between the sides = 14 cm
• Area (Triangle) = 120 cm²

To Find:

• Calculate the perimeter of the Triangle?

Solution:

Let the sides containing right angle be x

Again, (x - 14)cm

Then,

$\\ {\sf{ Area\: of\: Triangle = \left[ \dfrac{1}{2} \times x \times (x - 14) \right] cm^2 }}$

After putting Values,

we get;

$\\ \implies{\sf{ 120 = \dfrac{1}{2} x \times (x - 14) }} \\ \\ \implies{\sf{ x^2 - 14x - 240 = 0}} \\ \\ \implies{\sf{ x^2 - 24x + 10x - 240 }} \\ \\ \implies{\sf{ x(x-24) + 10(x-24) }} \\ \\ \implies{\sf{ (x-24)(x+10) = 0}} \\ \\ \implies{\sf{ x = 24}} \: \: \: \: \: \sf\purple{( neglecting\:x = -10)}$

One Side:- 24 cm

Other Side:- (24 - 14) = 10 cm

$\\ {\sf{ Hypotenuse = \sqrt{ (24)^2 + (10)^2 } cm }} \\ \implies{\sf{ \sqrt{ 576+100} cm }} \\ \implies{\sf\green{ \sqrt{676} cm}} \\ \implies{\sf{ 26 \: cm}}$

Perimeter of the Triangle;

$\\ \hookrightarrow\sf{ (24 + 10+ 26) cm} \\ \hookrightarrow\sf\large\orange{ 60cm}$

Hence,

The Perimeter of the Triangle is 60 cm.

$\sf\purple{\underline{\underline{Extra\: Dose:-}}}$

• ${\boxed{\sf\blue{ Area \ of\ Triangle = \dfrac{1}{2} \times Base \times altitude}}}$

• ${\boxed{\sf\red{ Perimeter \ of\ Triangle = a + b + c}}}$

• ${\boxed{\sf\orange{ (Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2}}}$