The lengths of the sides forming the right an | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The area of a right-angled triangle is given by the formula: $	ext{Area} = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$.Given,$	ext{base

Vedclass · Accepted Answer

$12 \, m, 14 \, m$

Vedclass · Answer

(C) The area of a right-angled triangle is given by the formula: $	ext{Area} = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$.Given,$	ext{base} = x \, m$ and $	ext{height} = (x+2) \, m$.$	ext{Area} = 84 \, m^2$.So,$84 = \frac{1}{2} 	imes x 	imes (x+2)$.$168 = x^2 + 2x$.$x^2 + 2x - 168 = 0$.Factoring the quadratic equation: $x^2 + 14x - 12x - 168 = 0$.$x(x+14) - 12(x+14) = 0$.$(x-12)(x+14) = 0$.Since the length cannot be negative,$x = 12$.The sides are $x = 12 \, m$ and $x+2 = 14 \, m$.

The lengths of the sides forming the right angle of a right-angled triangle are $x \, m$ and $(x+2) \, m$. If the area of the triangle is $84 \, m^2$,find the lengths of the sides which form the right angle.

Similar Questions

If both the roots of a quadratic equation $ax^2 + bx + c = 0$ $(a \neq 0)$ are equal,then ..... .

If $\ldots \ldots \ldots$ then real roots of a quadratic equation do not exist.

$A$ car takes $60$ minutes less for a journey of $150\,km$,if its speed is increased by $5\,km/hr$ from its usual speed. Find the original speed of the car in $km/hr$.

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $5x^{2} - 4\sqrt{5}x + 4 = 0$.

Which of the following polynomials does not have any real zero?

Vedclass Test Series

Exam Paper Generator

Online Exam Module