Triangle ABC is similar to triangle PQR and their perimeter is 36cm and 24cm respectively . If PQ =10cm find AB.
10 * (36/24)
= 30/2
= 15
no
To find AB, we need to determine the scale factor between the two triangles.
The scale factor can be calculated by dividing the perimeter of triangle ABC by the perimeter of triangle PQR.
Scale factor = Perimeter(ABC) / Perimeter(PQR)
In this case, the perimeter of triangle ABC is 36 cm, and the perimeter of triangle PQR is 24 cm.
Scale factor = 36 cm / 24 cm
Scale factor = 1.5
Now, we can use this scale factor to find the length of AB.
AB = PQ * Scale factor
AB = 10 cm * 1.5
AB = 15 cm
Therefore, the length of AB is 15 cm.
To find the length of AB, we can use the concept of similarity between triangles.
Similar triangles have the same shape but different sizes. The corresponding sides of similar triangles are in proportion to each other.
Given that triangle ABC is similar to triangle PQR, we can set up the proportion of their corresponding sides:
AB/PQ = BC/QR = AC/PR
We are given that PQ = 10 cm. Let's assume that AB is x cm.
So, the proportion becomes:
x/10 = BC/QR = AC/PR
To solve for x, we need to find the values of BC, QR, AC, and PR.
The perimeter of triangle ABC is given as 36 cm, which means the sum of its three sides is 36 cm. Similarly, the perimeter of triangle PQR is given as 24 cm.
From the given values, we can write the equations:
AB + BC + AC = 36 (Equation 1)
PQ + QR + PR = 24 (Equation 2)
Since PQ = 10 cm, we can rewrite Equation 2 as:
10 + QR + PR = 24
This simplifies to:
QR + PR = 14 (Equation 3)
Now, let's assume that BC is y cm and AC is z cm.
From the proportion, we can write:
x/10 = y/QR = z/PR
Rearranging Equation 3, we have:
PR = 14 - QR
Substituting this value in the proportion equation, we get:
x/10 = y/QR = z/(14 - QR)
Simplifying further, we have:
x = (10y)/QR = (z(10 - QR))/QR
From Equation 1, we have:
AB + BC + AC = 36
Substituting the values, we get:
x + y + z = 36
Now we have three equations:
x = (10y)/QR
z = (z(10 - QR))/QR
x + y + z = 36
From these equations, we can find the value of AB (x). However, solving this system of equations without specific values for BC, QR, AC, and PR is not possible.
So, in order to find AB, we need more information about the lengths of BC, QR, AC, and PR.