Question

Hi....

The base of the triangle is 4cm longer than its altitude.If the area of the triangle is 48cm. Then find its base and altitude.

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Answer 1

Hey Mate!
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Here is your answer :

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Let the altitude = x

Base = x + 4

Area of triangle = 1 /2 bh

$\frac{1}{2} \times (x + 4)x = 48 \\ \\ {x}^{2} + 4x = 48 \times 2 \\ \\ {x}^{2} + 4x = 96 \\ \\ {x}^{2} + 4x - 96 = 0 \\ \\ {x}^{2} + 12x - 8x - 96 = 0 \\ \\ x(x + 12) - 8(x + 12) = 0 \\ \\ x + 12 = 0 \: \: \: \: \: x - 8 = 0 \\ \\ x = - 12 \: \: \: \: \: \: x = 8$

Side never be negative.

Therefore,

Height = x = 8cm

Base = x + 4 = 8+ 4 = 12cm


HOPE THIS HELPS U...

Answer 2

The base of a triangle is 4 cm longer than its altitude. If the area of the triangle is 48 sq. cm, then find its base and altitude.



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Nikitha Mupparsi asked in Math

The base of a triangle is 4 cm longer than its altitude.Area is 48sq.cm Find base and altitude

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Pooja Khanna answered this
997 helpful votes in Math, Class IX

Area of triangle = 12×base×altitude

Given, area = 48 cm2

Let altitude be x cm, base = x + 4 cm

putting respective values in the  above given formula, we get

Area or triangle = 48 cm2⇒ 12× x × (x+4) = 48⇒ x × (x+4) = 96⇒ (x2+4x) = 96⇒ x2+4x−96 = 0⇒ x2+12x−8x−96 = 0⇒ x(x+12)−8(x+12) = 0⇒ (x−8) (x+12) = 0⇒ (x−8) = 0 or (x+12) = 0length cannot be negative so, x = 8.

Altitude = x = 8 cm

Base = x + 4 = 12 cm