Question

The area of
a triangle is 48 cm² . If its
height is
greater then the base by 4 cm find
the base?​

Answer 1

GiveN :

• Area of Triangle = 48 cm²
• Height is 4 cm greater than base.

To FinD :

• Magnitude of Base

SolutioN :

Area of right angles triangle is 48 cm² , height is 4cm greater than base.

Let, base be x cm. Then height will be x + 4 cm

Use formula for Area of Right Angled Triangle :

⇒Area = ½ * Base * Height

⇒48 = ½ * x * (x + 4)

⇒48 * 2 = x(x + 4)

⇒96 = x² + 4x

⇒x² + 4x - 96 = 0

Now, use Splitting the middle term Method

⇒x² + 12x - 8x - 96 = 0

⇒x(x + 12) - 8(x + 12) = 0

⇒(x + 12)(x - 8) = 0

⇒x = -12 , 8

So, we get there two values of Base : - 12 cm and 8 cm. Length can't be negative. So, Base will be taken as 8 cm

______________________

Proof :

⇒Height = x + 4

⇒8 + 4

⇒ 12 cm

Now, use formula for Area of Triangle

⇒ Area = ½ * Base * Height

⇒Area = ½ * 8 * 12

⇒48 = ½ * 96

⇒48 = 48

✯ Hence, our answer is correct

Answer 2

✯✯ QUESTION ✯✯

The area of a triangle is 48 cm² . If its height is greater then the base by 4 cm find the base?

━━━━━━━━━━━━━━━━━━━━

✰✰ ANSWER ✰✰

$\longmapsto\tt{Let\:the\:base\:be=x}$

➮As Given that its height is greater than its base by 4 : -

$\longmapsto\tt{Height=x+4}$

➥Using Formula : -

$\longmapsto\tt{\small{\boxed{\bold{\bold{\green{\sf{Area\:of\:Triangle=\dfrac{1}{2}\times{b}\times{h}}}}}}}}$

➥Putting Values : -

$\longmapsto\tt{48=\dfrac{1}{2}\times{x}\times{(x+4)}}$

$\longmapsto\tt{48=\dfrac{1}{2}\times{{x}^{2}}+4x}$

$\longmapsto\tt{48\times{2}={x}^{2}+4x}$

$\longmapsto\tt{96={x}^{2}+4x}$

$\longmapsto\tt{{x}^{2}+4x-96}$

➥Now , By splitting Middle Term : -

$\longmapsto\tt{{x}^{2}+4x-96=0}$

$\longmapsto\tt{{x}^{2}+12x-8x-96=0}$

$\longmapsto\tt{x(x+12)-8(x+12)=0}$

$\longmapsto\tt{(x-8)(x+12)=0}$

• x = 8
• x = -12

➮Here we get two values i.e. 8 and -12..Length can never be negative so base will be 8 cm..

➥Now ,

$\longmapsto\tt{Base=8\:cm}$

$\longmapsto\tt{Height=8+4}$

$\longmapsto\tt\bold{12\:cm}$

_______________________

✔VERIFICATION : -

$\longmapsto\tt{Area\:of\:triangle=\dfrac{1}{2}\times{b}\times{h}}$

$\longmapsto\tt{48=\dfrac{1}{2}\times{8}\times{12}}$

$\longmapsto\tt{48=\cancel\dfrac{96}{2}}$

$\longmapsto\tt\bold{48=48}$

✺ HENCE VERIFIED ✺