Question

In the figure here, Δ PQR is a RIGHT-ANGLED ISOSCELES triangle. PR = QR and PQ = 7 cm. The perimeter of the triangle is about 17 cm. Which of the following could be the AREA of the triangle?

Answer 1

Answer:

in isosceles triangle PR=QR and PQ=7 cm

so let the side PR is x and QR is also x

then the perimeter of triangle is 2x+7 =17

hence PR=QR=5cm

area of triangle is equal to 7√51/4

Answer 2

The area would be 12.5 cm square.

Step-by-step explanation:

It is given that Δ PQR is a right-angle triangle, which means, there is a right angle( 90-degree angle) present in the triangle.

Also, it is an isosceles triangle, hence, two sides must be equal. Given the equal sides are $PR = QR = x$

The other side $PQ = 7cm$

And the perimeter$=17cm$

Hence, we can write, the sum of sides = perimeter

$PQ + QR + PR = 17$

$7 + x + x = 17$

$7 + 2x = 17$

$2x = 17-7$

$2x = 10$

$x = 5 cm$

Thus, the area of the triangle

= half x base x altitude

$= \frac{1}{2}\times 5\times 5$

$=\frac{25}{2}$

$= 12.5 cm^2$