Diagram above,<SRP=<RPQ=90°<PSR=60° and PQR=45° if[SR]=3√2cm and [QR] =x find the value of x, leaving your answer in surd form
AAAaannndd the bot gets it wrong yet again!
in ∆SRP, SR = RP√3 so RP = 3√2/√3 = √6
In ∆RPQ, PQ = RP = √6
so x = RQ = RP√2 = √12
To solve this problem, we can use the fact that the measures of the angles in a triangle sum to 180°. Since we are given that the measures of three of the angles in triangle PQR are 90°, 60°, and 45°, we know that the measure of the fourth angle must be 180° - 90° - 60° - 45° = 45°.
Since all of the angles in triangle PQR are 45°, we know that triangle PQR is an isosceles right triangle. This means that the lengths of the two sides that form the right angle (QR and PR) are equal. Therefore, we can set QR = PR = x.
Since triangle PQR is a 45-45-90 triangle, we know that the lengths of the sides are in the ratio 1:1:√2. Therefore, we can set up the equation:
x/x = 1/√2
Solving for x, we find that x = x√2. Since x is positive, we can simplify this to x = √2x. Dividing both sides by √2, we find that x = x, which is always true. Therefore, the value of x is √2 cm.