Answer:
76.5 cm²
Step-by-step explanation:
Given the triangles are similar , then
ratio of sides = a : b , so
ratio of areas = a² : b²
Here ratio of sides = 9 : 13.5 = 2 : 3
ratio of areas = 2² : 3² = 4 : 9
let x be the area of Δ DEF and using proportion
=
( cross- multiply )
4x = 306 ( divide both sides by 4 )
x = 76.5
The area of Δ DEF = 76.5 cm²
Answer:
x = 4
Step-by-step explanation:
This is special right triangles
For the triangle on the bottom, the shorter leg is x, the longer leg is x * √3, and the hypotenuse is x *2. This means that the shorter leg is 2 since you the longer leg is that side multiplied by √3. The hypotenuse is x *2, which is 2 * 2 which equals 4.
Now we have one side of the bigger triangle. This triangle is a 45-45-90 triangle, and the rule is that the two legs are x, and the hypotenuse is x *2. Since we found a leg and not the hypotenuse of the bigger triangle, and the two legs are congruent, that means x is 4.
