Question

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

Answer 1

Answer:

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

Answer 2

Answer:

Height = 8 cm

Base = 12 cm

Step-by-step explanation:

Dimensions of Triangle:

Height = h

Base = (h + 4)

According to the Q,

>> Area of Triangle = 48 cm²

>> 1/2 * b * h = 48

>> 1/2 * (h + 4) * h = 48

>> (h + 4) * h = 48 * 2

>> h² + 4h = 96

>> h² + 4h - 96 = 0

Sum = 4

Product = -96

>> h² + 12h - 8h - 96

>> h (h + 12) - 8 (h + 12)

>> (h + 12) (h - 8)

.°. h + 12 = 0

>> h = -12 [Not Possible because Length cannot be negative]

.°. h - 8 = 0

>> h = 8

.°. Height:

>> h

>> 8 cm

.°. Base:

>> h + 4

>> 8 + 4

>> 12 cm

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