Question

the area of a triangle is equal to that of a square whose each sides measures 60 m. Find the side of the triangle whose corresponding altitude is 90m.

Answer 1

Area of Triangle = Area of Square
So, 1/2 * base * height = 60*60
sp, 90*base/2 = 3600
        45*base = 3600
            base(side) = 3600/45 = 1200/15 = 400/5 = 80 m 

Answer 2

$\underline{\textbf{Given That ..}}$

Area of Triangle = Area Of Square

And Each Side Of Square = 60m

So Now Let's Move For Solution ...

$\underline{\textbf{Solution..}}$

A/Q we need to find measure of side of triangle whose corresponding $\textbf{Altitude}$ measure 90m

So To Find This Follow The Simple Steps ...

$\underline{\textbf{Step - 1 ) Find Area Of Square }}$

We Know That

$\mathbf{Area \:Of\: Square\: = \underline{\:Side \:\times \:Side} }$

So In Question It's Given That

$\mathbf{Side\: Of \:Square\: = \: 60m}$

$\mathbf{ar(Square) \:= \: 60m\: \times \:60m \implies 3600{m}^{2} }$

Now In Question It's Also Said That ---

$\mathbf{Area \: Of \: Triangle \:= \: Area \:Of\: Square }$

Therefore We Have

$\mathbf{Area \: Of \: Triangle \:= \: Area \:Of\: Square\: = \: 3600{m}^{2}}$

$\underline{\textbf{Step - 2 ) Find The Measure Of Required Side }}$

Now From Above We Have Found That Area Of Triangle = 3600m^2 -- EQ ( 1 )

Now We Know That

$\mathbf{Area \:Of \:Triangle \: = \frac{1}{2} \times Base \times Height}$ --- EQ ( 3 )

And In Question It's Given That

Height = Altitude = 90m -- EQ ( 2 )

Now Putting Values Of EQ 1 And EQ 2 In EQ 3 We Have ....

$\mathbf{\frac{1}{2} \times Base \times 90m \: = 3600{m}^{2}}$

Now Taking 90m To RHS We Have

$\mathbf{\frac{1}{2} \times Base\: = 3600{m}^{2}\:/\:90m}$

$\mathbf{\Longrightarrow \frac{1}{2}\times Base\: = \:40m}$

Similarly Taking 1/2 To RHS We Have ...

$\mathbf{Base\: = \:40m\:\times\: 2 }$

Therefore We Have ....

$\mathbf{Base\: = \:Required \: Side \: = \:80m }$

$\underline{\textbf{Hence\:The\: Required\:Answer\: Is...}}$

$\boxed{\mathbf{80m}}$