construct a triangle PQR with base
PQ = 8.4 cm , angle P = 45 degree and
PR - QR = 2.8 cm
Construct a triangle PQR in which QR 8.4 angle Q 45°PR_PQ=2.8
To construct triangle PQR with the given information, follow these steps:
Step 1: Draw a line segment PQ of length 8.4 cm. This will be the base of the triangle.
Step 2: At point P, draw an angle of 45 degrees using a protractor. This will be the angle P.
Step 3: From point P, draw a line segment PR. The length of PR is not given, so we need to calculate it.
Step 4: Draw a line segment QR parallel to PQ and make it 2.8 cm shorter than PR. This means QR is 2.8 cm less than PR.
To calculate the length of PR, we can use the fact that QR is 2.8 cm shorter than PR. Let's assume the length of PR is x cm.
QR = PR - 2.8 cm
Since QR is 2.8 cm shorter than PR, we can write:
x - 2.8 = QR
Step 5: Use a ruler and measure the length of QR using the scale. Let's say you find QR to be y cm.
Now we have:
x - 2.8 = y
We have two equations:
QR = y
QR = PR - 2.8
Step 6: Solve the equations simultaneously to find the values of x and y.
Let's substitute QR = y into the equation QR = PR - 2.8:
y = x - 2.8
Now we have the two equations:
x - 2.8 = y
y = x - 2.8
Step 7: Solve the equations to find the values of x and y.
By simplifying the equations, we have:
x - y = 2.8 (Equation 1)
y = x - 2.8 (Equation 2)
Solving these equations will give us the values of x and y.
Step 8: Now, using the calculated values of x and y, mark point R on the line segment PR.
Step 9: Connect the points P, Q, and R to form triangle PQR.
Congratulations! You have successfully constructed triangle PQR with base PQ = 8.4 cm, angle P = 45 degrees, and PR - QR = 2.8 cm.