Question

The area of a triangle is 48cm2. If the altitude exceeds the
base by 4cm, then the base is:​

Answer 1

To find :-

• The base of the Triangle .

we have :-

• The Area of the Triangle = 48 cm² .
• The altitude of the Triangle exceeds the base by 4 cm . or, base of Triangle = ( altitude – 4 )

Formula used :-

Area of Triangle = 1/2 × Base × Height

Solution :-

• let altitude of the Triangle = x cm .
• as given in question that altitude is exceeds the base by 4 cm . so, base of the Triangle = ( x – 4 ) cm .

Area of Triangle = 1/2 × Base × Height

put the values of altitude and base and Area of Triangle in the formula we get :-

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

here, we have get the value of altitude .

• x = 12 or,
• x = – 8

• side never would be in negative .

Therefore, altitude of the Triangle is 12 cm .

so, base of the Triangle = ( altitude – 4 ) = 12 – 4 = 8 cm .

The required values of Altitude and Base of the Triangle is 12 cm and 8 cm respectively .

Answer 2

Answer:

Step-by-step explanation:

To find :-

The base of the Triangle .

we have :-

The Area of the Triangle = 48 cm² .

The altitude of the Triangle exceeds the base by 4 cm . or, base of Triangle = ( altitude – 4 )

Formula used :-

Area of Triangle = 1/2 × Base × Height

Solution :-

let altitude of the Triangle = x cm .

as given in question that altitude is exceeds the base by 4 cm . so, base of the Triangle = ( x – 4 ) cm .

Area of Triangle = 1/2 × Base × Height

put the values of altitude and base and Area of Triangle in the formula we get :-

here, we have get the value of altitude .

x = 12 or,

x = – 8

side never would be in negative .

Therefore, altitude of the Triangle is 12 cm .

so, base of the Triangle = ( altitude – 4 ) = 12 – 4 = 8 cm .

The required values of Altitude and Base of the Triangle is 12 cm and 8 cm respectively .