Question

The area of a right angle triangle is 600 square cm .if the base of the triangle exceeds the altitude by 10 cm ,find the base?

Answer 1

Hey

Here is ur answer.


it is given that
Area of right triangle =600cm2
Let base be x cm and altitude be y cm
And

x-y=10➖ 1
y=x-10➖ 2

Now
Area of right triangle = base * height /2
600= x*y/2
1200= x(x-10)
1200= x2- 10x
x2-10x-1200=0
By using quadratic formula
Then
D= b2- 4ac
D= 100+4800
D=4900
RootD= 70

Now
x= -b+rootD/2a
x= 10+70/2= 80/2= 40
And
x= -b-rootD/2a
x= -10-70/2= -80/2. = -40

base can't be negative
So x= 40cm is length of base

Hope it helps you

Answer 2

$\large{\underline{\bf{\pink{Answer:-}}}}$

✰ Base of triangle = 40cm

$\large{\underline{\bf{\blue{Explanation:-}}}}$

$\large{\underline{\bf{\green{Given:-}}}}$

✰ Area of triangle = 600sq cm

✰ Base exceeds the altitude by 10cm.

$\large{\underline{\bf{\green{To\:Find:-}}}}$

✰ we need to find the base of triangle .

$\huge{\underline{\bf{\red{Solution:-}}}}$

Let the altitude of the triangle be x cm.

Then,

it's base = (x + 10)cm.

Area of triangle.$:\implies\:\frac{1}{2}x(x+10)cm^2.$

$:\implies\:\frac{1}{2}x(x+10)=600$

$:\implies\:x(x+10)=1200$

$:\implies\:x^2+10x-1200$

$:\implies\:x^2+40x-30x-1200$

$:\implies\:x(x+40)-30(x+40)$

$:\implies\:(x+40)(x- 30)$

$:\implies\:x=-40\:or\:x=30$

$:\implies\:x=30$[altitude can't be negative]

Thus, the altitude of the triangle = 30cm.

And the base of the triangle = (30+10)cm

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 40cm.

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