Question

A triangle with a base of 8 meters has an area of 60 square meters.The longest side of the triangle is 17 meters.Is the triangle a right triangle?

Answer 1

Answer:

Yes, the triangle is a right triangle.

Step-by-step explanation:

A triangle with a base of 8 meters and longest side is 17 meters.

Area of triangle is $60\text{ m}^2.$

Let third side be x m

Semi-perimeter of triangle, $s=\dfrac{8+17+x}{2}=\dfrac{25+x}{2}$

Using Heron's formula to find area of triangle.

$\text{Area of triangle }=\sqrt{s(s-a)(s-b)(s-c)}$

$60=\sqrt{\dfrac{25+x}{2}\left(\dfrac{25+x}{2}-8\right)\left(\dfrac{25+x}{2}-17\right)\left(\dfrac{25+x}{2}-x\right)}$

squaring both sides

$3600=\dfrac{25+x}{2}\times \dfrac{x+9}{2}\times \dfrac{x-9}{2}\times \dfrac{25-x}{2}$

$3600=\dfrac{-50625+706x^{2}-x^{4}}{16}$

$x^4-706x^2+108225=0$

$(x^2-225)(x^2-481)=0$

$x^2=225\text{ or }x^2=481$

$x=\pm 15,\pm\sqrt{481}$

x should be positive integer.

So, $x=15\text{ m}$

Using pthagoreous theorem:

$17^2=15^2+8^2$

$289=225+64$

$289=289$

Therefore, the given triangle is a right triangle.