Question

The height of a right angled triangle is 49 cm more than the base. The area of the triangle is 330 cm square. Find the hypotenuse of the triangle.​

Answer 1

Let the base be a

So,the hieght is a+49

Area of triangle =1/2×b×h

330=1/2×a×(a+49)

330=1/2×(a²+49a)

a²+49a=660

a²+49a-660=0

a²+60a-11a-660=0

a(a+60)-11(a+60)=0

(a-11)(a+60)=0

a=11cm

Base=11cm

Hieght =11+49=60cm

By pythagoras theorem,

H²=P²+B²

H²=60²+11²

H²=3600+121

H=√3721

H=61cm

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Answer 2

let the base of the right triangle x cm

then height of the triangle = x + 49 c

$= > area = 330 \: c {m}^{2} \\ \\ = > \frac{1}{2} \times x \times (x + 49) = 330 \\ \\ = > {x}^{2} + 49x - 660 = 0 \\ \\ = > (x + 60)(x - 11) = 0 \\ \\ either \: x = - 60 \: or \: x = 11 \: \: \\ therefore \\ \: x = 11 \: cm \:( since \: length \: cannot \: be \: - ve) \\ \\ height \: = 11 + 49 = 60 \: cm \\ base = 11 \: cm \\ \\ = > hypotenuse= \sqrt{ {60}^{2} + {11}^{2} } \\ \\ = > hypotenuse= \sqrt{3721} \\ \\ = > hypotenuse \: = 61 \: cm$