Question

The area of a triangle is 48 cm2. find the base if the altitude exceeds the base by 4 cm.

Answer 1

Base of a triangle is 4 cm longer than its altitude.

Area of triangle =48 cm

2

Let base of triangle =b

Altitude =b−4

Area =

2

1

×b×h=48

2

1

×b×(b−4)=48

b

2

−4b−96=0

(b−12)(b+8)=0

But, base cannot be negative

So, base =12 cm

Altitude=12−4=8 cm.

thank you

Answer 2

Answer:

Base = 8 cm

Step-by-step explanation:

Let the base be x.

Altitude = x+4

Area of triangle = 1/2 × Base × Height

Given, area = 48 cm²

=> 48 = 1/2 × x × (x+4)

=> 96 = x²+4x

=> x²+4x-96 = 0

=> x²+12x-8x-96 = 0

=> x(x+12)-8(x+12) = 0

=> (x-8)(x+12) = 0

=> x = 8 or x = -12

Neglecting negative value of x.

Base = 8 cm

Altitude = (8+4) cm = 12 cm