Question

Area of a right triangle ABC is 120 sq feet. If ΔABC goes through a dilation transformation with a scale factor of 1.5, then what will be the area of the transformed triangle (in sq feet)?

• A. 220 sq feet
• B. 360 sq feet
• C. 270 sq feet
• D. 480 sq feet

Answer 1

The correct option is C 270 sq feet

It is given that the area of ΔABC = 120 sq units
And, scale factor = 1.5


Let $\Delta ABC$ be the preimage and $\Delta DEF$ the dilated image of $\Delta ABC$.
To calculate the area of $\Delta DEF$, we first need to calculate its base and height, i.e., b’ and h’, respectively
(Side length of the image = Scale factor × Corresponding side length of the preimage)
$\Rightarrow b^{\prime }=1.5\times b$ --------------- Equation 1
Similarly, $h^{\prime }=1.5\times h$ ---------------- Equation 2
Now,
Area of $\Delta DEF=½\times b^{\prime }\times h^{\prime }$ (Area of a right triangle $=½\times$ Base $\times$ Height, where base $=b^{\prime }$ and height $=h^{\prime })$
By putting equations 1 and 2 in the above formula of the area of $\Delta DEF$, we will get:
Area of $\Delta DEF=½\times (1.5\times b)\times (1.5\times h)=½\times b\times h\times 1.5\times 1.5$
$\Rightarrow \text{Area of}\Delta DEF=120\times 1.5\times 1.5\text{(Area of}\Delta ABC=120=½\times b\times h=120sqft)$
$\Rightarrow \text{Area of}\Delta DEF=120\times 2.25=270$ sq feet
Hence, the area of the transformed triangle is $270$ sq feet.
➡Option A is correct.