Question

The area of a right angles triangle is 165 m². Determine the measure of base and altitude if the measure of altitude is 7m more than the measure if base .​

Answer 1

$\huge{\underline{\underline{\mathfrak{\blue{Answer:-}}}}}$

Given,

Area of right angled triangle = 165m²

Altitude is 7m more than base

To find,

Measure of base and altitude.

Solution ,

Let the base be 'a'Then according to the condition given:

Altitude = a + 7 --------(1)

We know that area of triangle is :

⟹ ½ ×base×height

Also, we know that height of right angled triangle is its altitude.

So,

⇛ ½ × (a) × (a + 7) = 165

⇛ (a) × (a + 7) = 330

⇛a² + 7a = 330a

⇛a² + 7a - 330 = 0

Here we got a quadratic equation. Let us solve it by splitting the middle term method.

⇛ a² + 22a - 15a - 330 = 0

⇛ a(a + 22) -15(a + 22) = 0

⇛ (a + 22)(a -15) = 0

a = -22

a = -22a = 15

Here base can't be negative hence base = 15m

Putting a = 15 in (1) we get,

Altitude = 15 + 7 = 22

Hence,

Altitude = 22m

Base = 15m

${\huge{\orange{\ddot{\smile}}}}$

Answer 2

Let the measure of base be x m,

measure of altitude will be x+7 m

Area of right angled triangle = 165 m²

1/2 × b × h = 165

1/2 × x × x+7 = 165

x(x+7)/2 = 165

x²+7x = 330

x²+7x-330 = 0

x²+22x-15x-330 = 0

x(x+22)-15(x+22) = 0

(x+22)(x-15) = 0

x = -22 , x = 15

Measure of base = 15 m

Measure of altitude = 15+7 = 22 m

Hope it helps!!

Thank you ✌️