Question

The hypotenuse of a right triangle is 13 cm and the difference of remaining two sides is 7 cm. FInd the remaining two sides

Answer 1

Assuming x represents the length of the first side.

Use pythagorean theorem to solve:

a² + b² = c²

x² + (x+7)² = 13²

x² + x² + 14x + 49 = 169

2x² + 14x - 120 = 0

Solve the quadratic equation using the quadratic formula.

At the end, you will get side lengths of #(-14 ± 34) / 4, or -1² and 5.

Since a negative triangle length is impossible, 5 is the value of x and 5 + 7 is the value of x + 7, which makes 12.

The formula for area of a right triangle is A $= b \frac{h}{2}$

⇒ A $= \frac{b(h)}{2}$
⇒ A $= \frac{12(5)}{2}$

∴ A = 30 cm²

Hope This Helps :)

Answer 2

Answer:

Step-by-step explanation:

Hypotenuse=13cm

Let the 1st side be x

And the 2nd side (x+7)

Using pythagoras theorem

A²+B²=C²

x²+( x+7)²=13²

x² +x²+14x+49=169

2x²+14x-120=0(dividing by 2 we get)

x²+7x-60=0

x²-5x+12x-60=0

x(x-5) +12(x-5)=0

(x-5) (x+12 )=0

x=5 or x=-12

-12 is negative and therefore not applicable

X=5

Thus the sides of the triangle are

Hypotenuse=13cm (given)

1st side=x=5cm

2nd side=(x+7)=5+7=12cm