Question

Area of a triangle PQR right-angled at Q is 60 sq. cm. If the smallest side is 8cm long, find the length of the other two sides.

Answer 1

using pythagorous theorem....

Answer 2

The length of other two sides  of triangle PQR are 15 cm and 17 cm.

Step-by-step explanation:

Given,

Area of ΔPQR= 60 sq. cm.

Let QR be the smallest side and PQ  be the longest side and also the height of the triangle.

So, QR = 8 cm(base)

Now according to the formula of Area of triangle.

$Area = \frac{1}{2}\times base\times height$

$\frac{1}{2}\times8\times PQ=60\\\\4\times PQ=60\\\\PQ=\frac{60}{4}=15\ cm$

Since the triangle is right angled. So we use the Pythagoras Theorem to calculate the length of PR.

"The square of the hypotenuse is equal to the sum of the squares of other two sides".

$PR^2=PQ^2+QR^2\\\\PR^2=(15)^2+8^2\\\\PR^2=225+64=289$

Now taking square root on both side, we get;

$\sqrt{PR^2}=\sqrt{289}\\\\PR=17\ cm$

Hence the length of other two sides  of triangle PQR are 15 cm and 17 cm.