Question

the area of a right angles triangle is 165 m².
Determine the measure of base and altitude if the measure of altitude is 7m more than the measure if base .
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Answer 1

Base of the right angled
triangle (b)= x m
Altitude (h)=7m exceeds the base
h = ( x + 7 )m
Area of Right angled triangle
( A ) = 165 m² [ given ]

=> [x(x+7)]/2 = 165
=> x(x+7) = 230
=> x(x+7) = 15×22
=> x(x+7) = 15(15+7)
Compare both sides , we
conclude ,
x = 15
Therefore ,
base (b) = x = 15m
altitude (h) = (x + 7)
= 15 + 7
= 22 m

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Answer 2

Answer

Given,

• Area of right angled triangle = 165m²
• Altitude is 7m more than base

To find,

• Measure of base and altitude.

Solution ,

Let the base be 'a'

Then according to the condition given:

Altitude = a + 7 --------(1)

We know that area of triangle is :

$\implies \rm \frac { 1 } { 2 } × base × height$

Also, we know that height of right angled triangle is its altitude.

So,

⇛ $\rm \frac { 1 } { 2 } × (a) × (a + 7) = 165$

⇛ $\rm (a) × (a + 7) = 330$

⇛$\rm a^2 + 7a = 330$

⇛ $\rm a^2 + 7a - 330 = 0$

Here we got a quadratic equation. Let us solve it by splitting the middle term method.

⇛ $\rm a^2 + 22a - 15a - 330 = 0$

⇛ $\rm a(a + 22) -15(a + 22) = 0$

⇛ $\rm (a + 22)(a -15) = 0$

• a = -22
• a = 15

Here base can't be negative hence base = 15m

Putting a = 15 in (1) we get,

Altitude = 15 + 7 = 22

Hence,

• Altitude = 22m
• Base = 15m