The quotient of that problem is 30
Answer:
40 (cm)
Step-by-step explanation:
0. make up a new picture with additional elements (radius of the inscribed circle, it's 'x'; and some elements as shown in the attached picture);
1. the formula of the required perimeter is P=a+b+c, where c- hypotenuse.
2. apply the Pythagorean theorem: a²+b²=c², where c - hypotenuse, then calculate value of 'x' (attention! x>0, the length is positive value !)
3. substitute 'x' into the formula of the required perimeter. The result is 40.
PS. All the details are in the attached picture, answer is marked with red colour.
You started off very well. You identified the given and the pair of congruent sides.
Statement Reason
3. m<POM = m<NMO Alternate Interior Angles
4. m<NOM = m<PMO Alternate Interior Angles
5. ΔPMO ≅ ΔNOM ASA
6. MP ≅ NO CPCTC
Reasoning for statement 3: This is because MN ║PO and MO acts as a transversal.
Reasoning for statement 4: This is because MP ║NO and MO acts as a transversal.